Summary

A scalar quantity has only magnitude and no direction.

This means we can fully explain a scalar with a number
and a unit.

A vector quantity has both magnitude and
direction.

The distinction between scalars and vectors is important. We will use bold
face type to indicate a vector, such as r. In writing a vector by hand,
we will indicate a quantity is a vector by drawing an arrow above it as .
Some such distinguising notation is important. Do not write a vector
without some distinguishing characteristic or notation.

Consider adding two vectors together as in A + B
= C. Each vector can first be resolved into its
respective components,

A = (Ax , Ay ,
Az)

B = (Bx , By ,
Bz)

The components are then added as the scalars they are and the
new vector sum is reconstructed,

C = (Cx , Cy ,
Cz)

where

Cx = Ax + Bx

Cy = Ay + By

and

Cz = Az + Bz

We will often write this using unit vector notation
as

A = Axi + Ayj + Azk

B = Bxi + Byj +
Bzk

C = Cxi + Cyj +
Czk

where

Cx = Ax + Bx

Cy = Ay + By

and

Cz = Az + Bz

or

C = A + B

C = (Ax + Bx) i +
(Ay + By) j + (Az +
Bz) k

Two dimensional motion with constant acceleration can be handled
with vectors. The resulting motion is called projectile
motion and the path of an object undergoing such motion is a
parabola.

Projectile motion -- motion only under the influence of
gravity -- is a combination of

horizontal motion with constant velocity and

vertical motion with constant acceleration.

Uniform Circular Motion (UCM) is another example of
non-linear motion. UCM requires an acceleration directed toward
the center of the circle. This acceleration is called the
centripetal acceleration ("centripetal" means
center-seeking). This centripetal acceleration is